The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric-dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies. [S0031-9007(99) The van der Waals interaction plays an important role in characterizing ultracold collisions between two groundstate alkali-metal atoms. While the calculation of interaction coefficients has been a subject of great interest in atomic, molecular, and chemical physics for a very long time, it is only very recently that novel cold collision experiments, photoassociation spectroscopy, and analyses of magnetic field induced Feshbach resonances have yielded strict constraints on magnitudes of the coefficients. Moreover, due to the extreme sensitivity of elastic collisions to the long-range part of the potentials, knowledge of the van der Waals coefficients influences predictions of signs and magnitudes of scattering lengths determining stability of Bose-Einstein condensates. Although many theoretical methods have been developed over the years to calculate van der Waals coefficients, persistent discrepancies remain.In this paper, various relativistic ab initio methods are applied to determine the van der Waals coefficients for the alkali-metal dimers of Na to Fr [1]. As a check on our calculations, we also evaluate the atom-wall interaction constants and use them as a sensitive test of the quality of our wave functions. Furthermore, we calculate atomic polarizabilities and compare them to experimental data.The van der Waals interaction is the leading term of the potential energy between two ground-state alkalimetal atoms at long range. It arises from the interaction between induced dipole moments and is represented as 2C 6 ͞R 6 , where R is the distance between atoms. The dispersion coefficient C 6 can be conveniently expressed as an integral over dynamic polarizability at imaginary frequency a͑iv͒ (cf. [2]),The polarizability a͑iv͒ for a valence state jy͘ can be written as a sum over intermediate states jk͘,where the sum includes an integration over continuum states and R P N j 1 r j is the dipole operator for the Nelectron atomic system. We use atomic units throughout. The coefficient C 3 of the Lennard-Jones interaction between an atom and a perfectly conducting wall is (cf.[3])or, by explicit integration, C 3 1 12 ͗yjR ? Rjy͘ . (4) Using the latter relation, we have previously [4] determined the values of C 3 coefficients for alkali-metal atoms using many-body methods.The dipole operator R, being a one-particle operator, can have nonvanishing matrix elements for intermediate states represented by two types of Slate...

The dispersion coefficients C 6 , C 8 , and C 10 for the interactions between H, He, and Li are calculated using variational wave functions in Hylleraas basis sets with multiple exponential scale factors. With these highly correlated wave functions, significant improvements are made upon previous calculations and our results provide definitive values for these coefficients.

The electric dipole polarizabilities evaluated at imaginary frequencies for hydrogen, the alkali-metal atoms, the alkaline earth atoms, and the inert gases are tabulated along with the resulting values of the atomic static polarizabilities, the atom-surface interaction constants, and the dispersion (or van der Waals) constants for the homonuclear and the heteronuclear diatomic combinations of the atoms.

Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%.

The Casimir-Polder interaction between an atom and a metal wall is investigated under the influence of real conditions including the dynamic polarizability of the atom, finite conductivity of the wall metal, and nonzero temperature of the system. Both analytical and numerical results for the free energy and force are obtained over a wide range of atom-wall distances. Numerical computations are performed for an Au wall and metastable He * , Na, and Cs atoms. For the He * atom we demonstrate, as an illustration, that at short separations of about the Au plasma wavelength at room temperature the free energy deviates up to 35% and the force up to 57% from the classical Casimir-Polder result. Accordingly, such large deviations should be taken into account in precision experiments on atom-wall interactions. The combined account of different corrections to the Casimir-Polder interaction leads to the conclusion that at short separations the corrections due to the dynamic polarizability of an atom play a more important role than-and suppress-the corrections due to the nonideality of the metal wall. By comparison of the exact atomic polarizabilities with those in the framework of the single oscillator model, it is shown that the obtained asymptotic expressions enable calculation of the free energy and force for the atom-wall interaction under real conditions with a precision of 1%.